Problem: Simplify to lowest terms. $\dfrac{45}{30}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 45 and 30? $45 = 3\cdot3\cdot5$ $30 = 2\cdot3\cdot5$ $\mbox{GCD}(45, 30) = 3\cdot5 = 15$ $\dfrac{45}{30} = \dfrac{3 \cdot 15}{ 2\cdot 15}$ $\hphantom{\dfrac{45}{30}} = \dfrac{3}{2} \cdot \dfrac{15}{15}$ $\hphantom{\dfrac{45}{30}} = \dfrac{3}{2} \cdot 1$ $\hphantom{\dfrac{45}{30}} = \dfrac{3}{2}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{45}{30}= \dfrac{3\cdot15}{3\cdot10}= \dfrac{3\cdot 5\cdot3}{3\cdot 5\cdot2}= \dfrac{3}{2}$